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Comparison Geometry for Integral Radial Bakry-Émery Ricci Tensor Bounds
In this paper we prove mean curvature comparisons and volume comparisons on a smooth metric measure space when the integral radial Bakry-Émery Ricci...
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Bach-flat noncompact steady quasi-Einstein manifolds
The goal of this article is to study the geometry of Bach-flat noncompact steady quasi-Einstein manifolds. We show that a Bach-flat noncompact steady...
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Remarks on critical point metrics of the total scalar curvature functional
The aim of this short note is to study the space of metrics with constant scalar curvature satisfying the critical point equation on compact...
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Characterizations and integral formulae for generalized m-quasi-Einstein metrics
The aim of this paper is to present some structural equations for generalized m -quasi-Einstein metrics ( M n , g , ∇ f, λ ), which was defined recently...
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On conformal solutions of the Yamabe flow
The aim of this note is to define almost Yamabe solitons as special conformal solutions of the Yamabe flow. Moreover, we shall obtain some rigidity...
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Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons
The aim of this paper is to present a link between the Perelman potential for a compact Ricci soliton M n and the Hodge-de Rham decomposition...
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A new entropy formula for the linear heat equation
We give a monotonicity entropy formula for the linear heat equation on complete manifolds with Ricci curvature bounded from below. As its...
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Weak Closure of Singular Abelian L p -Bundles in 3 Dimensions
We prove the closure for the sequential weak L p -topology of the class of vector fields on B 3 having integer flux through almost every sphere. We...
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The geometry of closed conformal vector fields on Riemannian spaces
In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting...
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Estimate for index of hypersurfaces in spheres with null higher order mean curvature
In a recent paper (Barros, Sousa in: Kodai Math. J. 2009) the authors proved that closed oriented non-totally geodesic minimal hypersurfaces of the...
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Mixed Measures of Convex Cylinders and Quermass Densities of Boolean Models
Translative integral formulas for curvature measures of convex bodies were obtained by Schneider and Weil by introducing mixed measures of convex...
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Gelfand transforms and Crofton formulas
The term integral geometry has come to describe two different fields of research: one, geometrical, based on the works of Blaschke, Chern, and...
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Estimates on the Distribution of the Condition Number of Singular Matrices
We exhibit some new techniques to study volumes of tubes about algebraic varieties in complex projective spaces. We prove the existence of relations...
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Polynomial parallel volume, convexity and contact distributions of random sets
We characterize convexity of a random compact set X in ℝ d via polynomial expected parallel volume of X . The parallel volume of a compact set A is a...
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Subharmonicity of Higher Dimensional Exponential Transforms
Our main result states that the function (1 − E ρ is subharmonic, where 0 ≤ ρ ≤ 1 is a density function in ℝn, n ≥ 3,...
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Geometric Representations of Currents and Distributions
Currents are defined abstractly as dual spaces to differential forms and differential forms are defined abstractly as dual spaces to linear spaces of...
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Curvatures and Currents for Unions of Sets with Positive Reach, II
A class of subsets of ℝ d which can berepresented as locally finite unions of sets with positive reach isconsidered. It plays a role in PDE's on...
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On hypersurfaces inR n+1 with integral bounds on curvature
We show that the L p norm of the second fundamental form of hypersurfaces in R n +1 is very coercive in the GMT setting of Gauss graphs currents, when p...